Abstract Submitted for the OSS13 Meeting of The American Physical Society
The Real Meaning of the Spacetime-Interval FLORENTIN SMARANDACHE, University of New Mexico — The spacetime interval is measured in light-meters. One light-meter means the time it takes the light to go one meter, i.e. 3 · 10−9 seconds. One can rewrite the spacetime interval as: ∆s2 = c2 (∆t)2 − [(∆x)2 + (∆y)2 + (∆z)2 ]. There are three possibilities: a)∆s2 =0 which means that the Euclidean distance L1 L2 between locations L1 and L2 is travelled by light in exactly the elapsed time ∆t. The events of coordinates (x, y, z, t) in this case form the so-called light cone. b)∆s2 > 0 which means that light travels an Euclidean distance √ greater than L1 L2 in the elapsed time ∆t. The below quantity in meters: ∆s = c2 (∆t)2 − [(∆x)2 + (∆y)2 + (∆z)2 ] means that light travels further than L2 in the prolongation of the straight line L1 L2 within the elapsed time ∆t. The events in this second case form the time-like region. c)∆s2 < 0 which means that light √ travels less on the straight line L1 L2 . The below quantity, in meters: -∆s = −c2 (∆t)2 + [(∆x)2 + (∆y)2 + (∆z)2 ] means how much Euclidean distance is missing to the travelling light on straight line L1 L2 , starting from L1 in order to reach L2 . The events in this third case form the space-like region. We consider a diagram with the location represented by a horizontal axis (L) on [0, ∞), the time represented by a vertical axis (t) on [0, ∞), perpendicular on (L), and the spacetime distance represented by an axis (∆s) perpendicular on the plane of the previous two axes. Axis (∆s) from [0, ∞) is extended down as (−∆s) on [0, ∞).
Florentin Smarandache University of New Mexico Date submitted: 04 Mar 2013
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